Question 1:
(a) State if each of the following statements is true or false.
(i) ${2}^{4}=16\text{and}12\xf7\sqrt[3]{27}=3.$
(ii) 17 is a prime number or an even number.
(b) Complete the statement, in the answer space, to form a true statement by
using the quantifier ‘all’ or ‘some’.
(c) Write down two implications based on the following statement:
Solution:
(a)(i) False
(a)(ii) True
(b) Some multiples of 3 are multiples of 6.
(c) Implication 1: If a number is a prime number, then it is only divisible by 1
and itself.
Implication 2: If a number is only divisible by 1 and itself, then it is a prime
number.
(a) State if each of the following statements is true or false.
(i) ${2}^{4}=16\text{and}12\xf7\sqrt[3]{27}=3.$
(ii) 17 is a prime number or an even number.
(b) Complete the statement, in the answer space, to form a true statement by
using the quantifier ‘all’ or ‘some’.
(c) Write down two implications based on the following statement:
A
number is a prime number if and only if it is only divisible by 1 and itself.

Solution:
(a)(i) False
(a)(ii) True
(b) Some multiples of 3 are multiples of 6.
(c) Implication 1: If a number is a prime number, then it is only divisible by 1
and itself.
Implication 2: If a number is only divisible by 1 and itself, then it is a prime
number.
Question 2:
(a) State if each of the following statements is true or false.
(i) 2 × 3 = 6 or 2 + 3 = 6
(ii) 2 is a prime number and 5 is an even number.
(b) Write down the converse of the following implication.
Hence, state whether the converse is true or false.
Solution:
(a)(i) True
(a)(ii) False
(b) Converse: If x is a multiple of 3, then x is a multiple of 12.
The converse is false.
(c) Premise 2: ABCDEF is a hexagon.
(a) State if each of the following statements is true or false.
(i) 2 × 3 = 6 or 2 + 3 = 6
(ii) 2 is a prime number and 5 is an even number.
(b) Write down the converse of the following implication.
Hence, state whether the converse is true or false.
If
x is a multiple of 12,
then
x is a multiple of 3.

(c) Complete the premise in the following argument:
Premise 1: All hexagons
have six sides
Premise 2: _____________________
Conclusion: ABCDEF has six sides.

(a)(i) True
(a)(ii) False
(b) Converse: If x is a multiple of 3, then x is a multiple of 12.
The converse is false.
(c) Premise 2: ABCDEF is a hexagon.
Question 3:
(a) Complete each of the following statements with the quantifier ‘all’ or ‘some’
so that it will become a true statement.
(i) ___________ of the prime numbers are odd numbers.
(ii) ___________ pentagons have five sides.
(b) Write down two implications based on the following statement:
(c) Complete the premise in the following argument:
Solution:
(a)(i) Some of the prime numbers are odd numbers.
(a)(ii) All pentagons have five sides.
(b) Implication 1: If A ∩ B = B, then A υ B = A.
Implication 2: If A υ B = A, then A ∩ B = B.
(a) Complete each of the following statements with the quantifier ‘all’ or ‘some’
so that it will become a true statement.
(i) ___________ of the prime numbers are odd numbers.
(ii) ___________ pentagons have five sides.
(b) Write down two implications based on the following statement:
A ∩ B = B if
and only if A υ B = A.

(c) Complete the premise in the following argument:
Premise 1: If a number
is a factor of 24, then it is a factor of 48.
Premise 2: 12 is a
factor of 24.
Conclusion: _____________________

Solution:
(a)(i) Some of the prime numbers are odd numbers.
(a)(ii) All pentagons have five sides.
(b) Implication 1: If A ∩ B = B, then A υ B = A.
Implication 2: If A υ B = A, then A ∩ B = B.
(c) Conclusion: 12 is a factor of 48.